Pseudorandom encoding of complex-valued functions onto amplitude-coupled phase modulators

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Abstract
Pseudorandom encoding is a method of statistically approximating desired complex values with those values that are achievable with a given spatial light modulator. Originally developed for phase-only modulators, pseudorandom encoding is extended to modulators for which amplitude is a function of phase. This is accomplished by transforming the phase statistics to compensate for the amplitude coupling. Example encoding formulas are derived, evaluated, and compared with a noncompensating pseudorandom-encoding algorithm. Compensating algorithms encode a smaller area of the complex plane and can produce more noise than is possible for arbitrary pseudorandom algorithms. However, the encoding formulas have greatly simplified numerical implementations.